\( \int x e^{-x} d x \)

Step 1 ：Perform integration by parts: let \(u=x\) and \(dv=e^{-x}dx\), then \(du=dx\) and \(v=-e^{-x}\)

Step 2 ：Apply the integration by parts formula: \(\int x e^{-x} d x = -x e^{-x} - \int(-e^{-x})dx\)

Step 3 ：Evaluate the integral: \(\int x e^{-x} d x = -x e^{-x} + e^{-x} + C\)